    Graph theory has gradually become an essential part of computer science [1]}, [2]}, [3]} as well as network analysis [4]}, [5]}, [6]}, [7]} (see also [8]} for a recent review on applications in physics). We firmly believe that the theory and results presented here will be useful to the community working on network analysis and applications of quantum information theory to quantum condensed matter physics (such as TEE), apart from its use within the graph theory community.
